{"paper":{"title":"Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Hyperbolic graph neural networks outperform Euclidean ones only when the task itself requires preserving the graph's metric structure.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Dionisia Naddeo, Geri Skenderi, Jonas Linkerh\\\"agner, Nicola Toschi, Veronica Lachi","submitted_at":"2026-02-02T09:01:58Z","abstract_excerpt":"Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely adopted as a principled choice for representation learning on tree-like graphs. In this work, we question this paradigm by proposing the additional condition of geometry--task alignment, i.e., whether the metric structure of the target follows that of the input graph. We theoretically and empirically demonstrate the capability of HGNNs to recover low-distortion"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"HGNNs gain an advantage on link prediction, a naturally geometry-aligned task, whereas this advantage largely disappears on standard node classification benchmarks, which are typically not geometry-aligned.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That link prediction is inherently geometry-aligned while standard node classification benchmarks are not, and that the chosen distortion measures and benchmarks generalize beyond the tested cases.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"HGNNs recover low-distortion representations and outperform Euclidean models only on geometry-aligned tasks such as link prediction, while the advantage disappears on non-aligned tasks like node classification.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hyperbolic graph neural networks outperform Euclidean ones only when the task itself requires preserving the graph's metric structure.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fb924015bf0306b207d0c86b23b963ab80d84645c6044bff35b6622be71b4df0"},"source":{"id":"2602.01828","kind":"arxiv","version":2},"verdict":{"id":"31c5d020-03ee-4a94-9849-10605a5fe56e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T08:47:46.604918Z","strongest_claim":"HGNNs gain an advantage on link prediction, a naturally geometry-aligned task, whereas this advantage largely disappears on standard node classification benchmarks, which are typically not geometry-aligned.","one_line_summary":"HGNNs recover low-distortion representations and outperform Euclidean models only on geometry-aligned tasks such as link prediction, while the advantage disappears on non-aligned tasks like node classification.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That link prediction is inherently geometry-aligned while standard node classification benchmarks are not, and that the chosen distortion measures and benchmarks generalize beyond the tested cases.","pith_extraction_headline":"Hyperbolic graph neural networks outperform Euclidean ones only when the task itself requires preserving the graph's metric structure."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"4017e771db8931486e527eba68561fd1892cc6b6950a62b8bdaeb95f3e6616dd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}